@article{RieraGogolinEisert2012,
  author    = {Riera, Arnau and Gogolin, Christian and Eisert, Jens},
  title     = {Thermalization in nature and on a quantum computer},
  series = {Physical review letters},
  volume    = {108},
  journal   = {Physical review letters},
  number    = {8},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {0031-9007},
  doi       = {10.1103/PhysRevLett.108.080402},
  pages     = {5},
  year      = {2012},
  abstract  = {In this work, we show how Gibbs or thermal states appear dynamically in closed quantum many-body systems, building on the program of dynamical typicality. We introduce a novel perturbation theorem for physically relevant weak system-bath couplings that is applicable even in the thermodynamic limit. We identify conditions under which thermalization happens and discuss the underlying physics. Based on these results, we also present a fully general quantum algorithm for preparing Gibbs states on a quantum computer with a certified runtime and error bound. This complements quantum Metropolis algorithms, which are expected to be efficient but have no known runtime estimates and only work for local Hamiltonians.},
  language  = {en}
}
@article{JanottaGogolinBarrettetal.2011,
  author    = {Janotta, Peter and Gogolin, Christian and Barrett, Jonathan and Brunner, Nicolas},
  title     = {Limits on nonlocal correlations from the structure of the local state space},
  series = {New journal of physics : the open-access journal for physics},
  volume    = {13},
  journal   = {New journal of physics : the open-access journal for physics},
  number    = {23},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {1367-2630},
  doi       = {10.1088/1367-2630/13/6/063024},
  pages     = {24},
  year      = {2011},
  abstract  = {The outcomes of measurements on entangled quantum systems can be nonlocally correlated. However, while it is easy to write down toy theories allowing arbitrary nonlocal correlations, those allowed in quantum mechanics are limited. Quantum correlations cannot, for example, violate a principle known as macroscopic locality, which implies that they cannot violate Tsirelson's bound. This paper shows that there is a connection between the strength of nonlocal correlations in a physical theory and the structure of the state spaces of individual systems. This is illustrated by a family of models in which local state spaces are regular polygons, where a natural analogue of a maximally entangled state of two systems exists. We characterize the nonlocal correlations obtainable from such states. The family allows us to study the transition between classical, quantum and super-quantum correlations by varying only the local state space. We show that the strength of nonlocal correlations-in particular whether the maximally entangled state violates Tsirelson's bound or not-depends crucially on a simple geometric property of the local state space, known as strong self-duality. This result is seen to be a special case of a general theorem, which states that a broad class of entangled states in probabilistic theories-including, by extension, all bipartite classical and quantum states-cannot violate macroscopic locality. Finally, our results show that models exist that are locally almost indistinguishable from quantum mechanics, but can nevertheless generate maximally nonlocal correlations.},
  language  = {en}
}
@article{GogolinMuellerEisert2011,
  author    = {Gogolin, Christian and M{\"u}ller, Markus P. and Eisert, Jens},
  title     = {Absence of thermalization in nonintegrable systems},
  series = {Physical review letters},
  volume    = {106},
  journal   = {Physical review letters},
  number    = {4},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {0031-9007},
  doi       = {10.1103/PhysRevLett.106.040401},
  pages     = {4},
  year      = {2011},
  abstract  = {We establish a link between unitary relaxation dynamics after a quench in closed many-body systems and the entanglement in the energy eigenbasis. We find that even if reduced states equilibrate, they can have memory on the initial conditions even in certain models that are far from integrable. We show that in such situations the equilibrium states are still described by a maximum entropy or generalized Gibbs ensemble, regardless of whether a model is integrable or not, thereby contributing to a recent debate. In addition, we discuss individual aspects of the thermalization process, comment on the role of Anderson localization, and collect and compare different notions of integrability.},
  language  = {en}
}